Question

The power , or loudness, of sound is measured on a scale of increased by a factor of 100$(={10}^2$), the sound is called twice as loud and when it increases 10,000 $(={10}^4)$ times it is called four times as loud. The exponent of ten is called a bel and one decible is one tenth of a bel. Zero decible is chosen as the intensity of the slowest sound which is just audible or is on the threshold of hearing whereas the intensity of loudest sound is about 170 decibel. A sound of 60 decibel is ......... times more intense than a sound of 40 decibel :

• A. 20
• B. 100
• C. ${10}^{20}$
• D. none of these

Answer 1

The correct option is B 100

Loudness of two sounds are given as $L_2=60dB$ and $L_1=40dB$

Loudness of sound $L=10{\log }_{10}\frac{I}{I_o}$

$⟹$ $L_2-L_1=10{\log }_{10}\frac{I_2}{I_1}$

Or $60-40=10{\log }_{10}\frac{I_2}{I_1}$

Or ${\log }_{10}\frac{I_2}{I_1}=2$

Or $\frac{I_2}{I_1}={10}^2=100$

Thus $60dB$ sound is $100$ times more intense than $40dB$ sound.